Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin–orbit interaction

Abstract

We examine the effect of non-equilibrium processes modeled by the introduction of a generalized Boltzmann factor on the thermal and magnetic properties of an array of two-dimensional GaAs quantum dots in the presence of an external uniform and constant magnetic field. The model consists of a single-electron subject to a confining Gaussian potential with a spin-orbit interaction in the Rashba approach. We compute the specific heat and the magnetic susceptibility within the formalism of χ 2 -superstatistics from the exact solution of the Schrödinger equation. Furthermore, an analytic solution for the partition function allows a study of the impact of the number of subsystems on the superstatistical corrections and confirms that the ordinary thermo-magnetic properties are recovered whenever the thermal distribution can be approximated by a Dirac delta. Also, we found a progressive disappearance of the Schottky anomaly with decreasing number of subsystems, while the specific heat ceases to be a monotonically increasing function with respect to the average temperature when the χ 2 -distribution is spread over a large range of temperatures. Remarkably, the introduction of fluctuations in the temperature is found to suppress the paramagnetic phase transition that would otherwise appear at low temperatures. Finally, we emphasize that an appropriate construction of the definition of physical observables is crucial for obtaining a correct description of the physics derived from a non-extensive construction of the entropy.

Superstatistics of the one-dimensional Klein-Gordon oscillator with energy-dependent potentials

“…In our case, we are focused on Gamma distribution defined by Eq. (16): this choice is justified by the wide use of this distribution in the literature: as an example, we can cite the following: in blinking quantum dots, cosmic ray statistics, various scattering processes in particle physics [9], one-dimensional Dirac oscillator [7] and the thermo-magnetic properties of a system of 2D GaAs quantum dots [34]. Other recent applications of the superstatistics are briefly reviewed by Refs.…”

“…In the recent paper of Castaño et al [34], the authors used the q-algorithm of the q-calculus formalism [22,23] to discuss thermo-magnetic properties of a system of 2D GaAs quantum dots. Here we can mention two remarks about this formalism:…”

Super-statistics and quantum entanglement in the isotropic spin-1/2 XX dimmer from a non-additive thermodynamics perspective

“…As shown in previous works [9,21],admitting parallelism between SS and non-extensive thermodynamics has profound implications in the energy constraints to let invariant the Legendre structure (LS) behind a thermal treatment. Although the computation of quantum entanglement in Ref.…”

“…Super-statistics (SS), developed by Beck and Cohen, is an effective way to study the non-equilibrium processes based on the idea that the thermodynamics of a system that passes through several equilibrium thermodynamic states or is divided into subsystems, each in local equilibrium, can be approximated by postulating an average Boltzmann factor weighted with the density probability function of fluctuations [1][2][3]. It has been applied to many topics: turbulence models [4,5], cosmic rays [6], quantum cromodynamics [7,8], quantum dots [9,10], out-of-equilibrium Ising models [11], quantum field theory [12,13], among others [14][15][16][17]. Then, SS is a subject that deserves attention.…”

Thermodynamic relations and fluctuations in the Tsallis statistics

“…It is considered that the Legendre transform structure is an essential ingradient [12]. In contranst, it is rarely noted that the Legendre transform structure may be unneccesary in the unconventional statistics [13]. It was also shown that the Legendre transform structure is robust against the choice of entropy and the definition of mean value [12,14].…”